Question 1 The Fourier transform of a waveform v(t) is given by V( omega )= int_(- infty )^( infty ) v(t)exp(-j omega t)dt. For the voltage pulse v(t) shown in Fig. 1, (a) Show that its Fourier transform V(f)=2sinc(2f)-0.5sinc(f), where the sinc function is defined as sinc(x)=sin( pi x)/( pi x). (14 marks) (b) Calculate the magnitude of V(f) in dB solutionspile.com

Question

Question 1 The Fourier transform of a waveform

v(t)

is given by

V(\omega )=\int_(-\infty )^(\infty ) v(t)exp(-j\omega t)dt

. For the voltage pulse

v(t)

shown in Fig. 1, (a) Show that its Fourier transform

V(f)=2sinc(2f)-0.5sinc(f)

, where the sinc function is defined as

sinc(x)=sin(\pi x)/(\pi x)

. (14 marks) (b) Calculate the magnitude of

V(f)

in

dB(V)/(H)z

at 0.5 Hz . (3 marks) (c) Calculate the normalised energy spectral density at 0.5 Hz . (d) The pulse area is equal to

V(0)

. Calculate the pulse area and verify the result using time integration. (5 marks) Fig. 1. Waveform of Question 1(a).

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Expert Answer to -  Question 1 The Fourier transform of a waveform v(t) is given by V( omega )= int_(- infty )^( infty

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Solution for -  Question 1 The Fourier transform of a waveform v(t) is given by V( omega )= int_(- infty )^( infty

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This an additional answer to -  Question 1 The Fourier transform of a waveform v(t) is given by V( omega )= int_(- infty )^( infty

(Solved): Question 1 The Fourier transform of a waveform v(t) is given by V(\omega )=\int_(-\infty )^(\infty ...